Course syllabus

Matematik - System och transformer
Mathematics - Systems and Transforms

FMAF05, 7 credits, G2 (First Cycle)

Valid for: 2015/16
Decided by: Education Board B
Date of Decision: 2015-04-16

General Information

Main field: Technology.
Compulsory for: E2, F2, I2, Pi2
Elective Compulsory for: D2
Elective for: BME4, C4, N3
Language of instruction: The course will be given in Swedish


The aim of the course is to present mathematical concepts and methods from linear algebra and analysis which are important in systems theory (continuous and discrete), and for further studies within e.g. mathematics, economy, physics, mathematical statistics, mechanics, control theory, signal theory and for future professional work. The aim is also to develop the student's ability to solve problems, to assimilate mathematical text and to communicate mathematics.

Learning outcomes

Knowledge and understanding
For a passing grade the student must



Competences and skills
For a passing grade the student must




Linear algebra: Spectral theory, quadratic forms.

Systems of linear differential equations: Equations in state form. Solution via diagonalization. Stability. Stationary solutions and transients. Solution via exponential matrix.

Input/output relations: Linearity, time and space invariance, stability, causality. Convolutions. Elementary distribution theory. Transfer and frequency functions. Discrete systems.

Fourier analysis: The Laplace and Fourier transforms. Inversion formulae, the convolution theorem and Plancherel's theorem. Transform theory and analytic functions. Applications to differential equations and systems of differential equations.

Examination details

Grading scale: TH
Assessment: Written test comprising theory and problem solving. Computer work and written assignements should be completed BEFORE the exam.

Code: 0108. Name: Systems and Transforms.
Credits: 7. Grading scale: TH.
Code: 0208. Name: Computer Work.
Credits: 0. Grading scale: UG.


Admission requirements:

Required prior knowledge: FMAF01 Analytic functions.
The number of participants is limited to: No
The course overlaps following course/s: FMA030, FMA036, FMA062, FMA450, FMAF10

Reading list

Contact and other information

Course coordinator: Studierektor Anders Holst,
Course homepage:
Further information: The written exams for this course may also be used as written exams on the earlier courses FMA450 and FMA036. In order for an exam to be graded it is necessary that the examinee has passed on the assignments and the computer sessions before the exam.